3D finite difference modeling of controlled-source electromagnetic response in frequency domain based on a modified curl-curl equation

Abstract

3D controlled-source electromagnetic (CSEM) modeling involves the solution of the Maxwell's curl-curl equations, which have abundant null space. This is commonly handled by adding one additional iteration of divergence correction after each certain iterations of the solution process of the curl-curl equations (CC-DC). Its efficiency typically deteriorates as lower frequencies are used. In this paper, we propose a 3D finite difference CSEM modeling algorithm based on a modified version of the curl-curl equations with scaled grad-div operator (CCGD) in frequency domain. In this approach, we integrate the divergence correction term in the original system with its importance controlled by scaling factors (the same values as model resistivities are used in this paper) and avoid the application of the iterative divergence correction. The accuracy of the proposed approach is verified using a layered model due to the existence of analytical solution for the simple model. Then based on two more complex synthetic models, we examine the numerical performance of the CCGD approach, and compare it with the traditional CC-DC approach in terms of computing time and iteration number. The results indicate that the proposed CCGD approach is efficient and stable over different frequencies.